Exercise 2 - Visualizing and Refining our terrain survey

Introduction

Exercise 2 is a continuation of exercise 1. For this exercise we were to take the data from exercise 1 and import it into AcrGIS.  Once we had the data correctly formatted for use we were tasked to run several spatial interpolation tools.

Interpolation is a method of estimating surface values from unsampled points based on known points, such as the data we collected in exercise 1.  The result is the creation of a fully rendered and filled surface that can be viewed in 3 dimensions in ArcScene as can be seen below.  Since it is not realistic, or even necessary to take measurements from every possible space in a desired area, interpolation is used to create what amount to guesses based on the data sample it is given.  As will be discussed below, the higher resolution data will result in better interpolation.

There are other factors that effect the quality and accuracy of interpolation.  Mainly you must know the result that is desired, so that the correct method can be used.  Certain methods, like Inverse Distance Weighting and Natural Neighbor, use close by points to make their guesses.  Still others, like Kriging, use a geostatistical method to make their determinations.

Methods

In exercise 1 we were tasked to create a terrain surface model.  We used flower boxes located in the courtyard of Phillips hall as the study area for our surface model.  While there was an amount of soil present in the flower box, it frozen hard and we opted to use the snow that was covering the surface.

Our flower box was required to have the following features: Ridge, Hill, Depression, Valley, and a Plain.   Our group had no ideas of known places we could recreate, so we settled with laying our the features as they would fit in the flower box.  As can be seen in below in figure 1, we created a hill near the center of our model, with a plain and depression in the foreground, and the valley and ridge toward the top of the flower box.

Once we had our model the way we wanted it we devised our survey techniques.  We needed a way to collect point in XY coordinates with Z being used to display our elevation.  Our flower box had boards on the sides to contain the soil and plants grown there during the summer, and we decided to make use of this for our survey.

When we created our features we made sure that none of them went above the surface of the side boards.  The flower box has a 2:1 aspect ratio, meaning the length was twice the width.  We wanted to have a grid that was 10x20, which would give us 200 points.  Since the box was 2.4m by 1.2, we began by placing pins every 12cm along the sides of our model.  We then ran rows of twine down the length of the box but ran out of string after 9 1/2 rows.  We decided to improvise by using the half row, held by a teammate at each end, to move down it along the width as we measured each row.

When we began to measure we just read off the distance in cm's from the string to where our meter stick first touched our surface.  All points were collected from the upper left corner of each grid square as seen in figure 1.  While one person read off measurements another person recorded them in a notebook the had a corresponding grid created in it.  This method proved efficient and effective for the scale of the survey we were doing.

Figure 1. Using a meter stick to collect points along our grid.  We ran out of twine to cover the length, so we used a half piece to move along the width as each row was collected.

One miscalculation was not accounting a bordering line on the grid.  The result of this is that we lose one row on the width and another on the length.  This reduced our total point count to 171 points total.

The next thing we found out was that we need to "massage" our data to get it into the correct format to be imported.  The term "massage" is used because we are not really changing any of the actual data, just how it is presented and imported.  In our case we had to make all the values negative, since our survey was measured from the top-down.  If we did not do this, our elevation values would create an inverted surface - i.e. the hills would become depressions, ridges - valleys, etc.  This was simple to do in Excel.  Then the data was imported into ArcGIS and we created our point feature class.  A point feature class is a 2d layer of dots on a surface.  We then used 3D Analyst tools to create a several interpolation surfaces.

Discussion

Below are several Interpolation techniques displayed in 2D and 3D.

Figure 2. Our terrain model from exercise 1 for reference. In the center is our hill. At the base of our hill on the far side is our valley. Farther in the background is our ridge, it begins on the left and forms a Y shape toward the corner. In the foreground covering the left portion is our plain, and our depression forming in the lower right corner of our model. 

First is Inverse Distance weighted or IDW.  IDW is an interpolation method that uses Tobler's first law of Geography- that near things are more alike than things that are far apart- to make assumptions about the data given.  It uses the closest measured values as an influence on the next nearest point.  An important feature of IDW is that as it creates the surface, it does not pass through any of the actual points.

Figure 3. 2D IDW model.Points are weighted for interpolation to allow the influence of one point relative to another to be controlled by the distance, in an inverse relationship, i.e. nearer has more influence than farther points.

Figure 4. Inverse-distance weighting.  In this 3D view we can see how smooth the plain is on the left, but more prominent are the pointy peaks that should form the ridge on the right side.

Figure 5. IDW in 3D model. The odd shapes seen along the top part are due to the resolution being so low, as well as the type of interpolation being used.  Since one value is very high, and others near it are very low, it shows a steeper slope than it would in other methods.

Next is a method of Interpolation known as Kriging.  Kriging uses a geostatistical formula to calculate the statistical relationship between the points that are measured.  The assumption is that there is some spatial correlation that can explain the variations found in the surface and that it is consistent across the spatial extent.  This method shows less vertical exaggeration in this configuration than other methods show, but there is still in impression of what is going on.

Figure 6. 3D side view of model using Kriging.  The central valley has almost disappeared from the model, along with the ridge line that should be seen in the right corner.  There is also less vertical exaggeration to be seen in this model.

Figure 7. 3D model using Kriging
method of interpolation.  The steep drops and rises that exist in the real world surface as well as other models are averaged out as a part of this method.

Figure 8. 2D model using Kriging method.  while this gives some impression of the elevation in the surface, red being higher and yellow to green being lower, it is not accurate as can be seen in other methods. 

The third method of interpolation used is called natural neighbor.  Natural neighbor finds the closest subset of samples and applies a weight to them based on their associated position in a Thiessen polygon.  It seems to be related to IDW, but here the amount of scatter point influence is defined by the local coordinates of the data set.  Natural Neighbor works well when scatter points are clustered in the data set.

Figure 9.  3D side model using Natural neighbor interpolation. Very peaked view. It would be difficult to guess the feature on the right is supposed to be a ridge.

Figure 10. Natural neighbor method.
Seems to be less smooth than other methods, while still showing exaggerated peaks. 

Figure 11.  2D view from
above of natural neighbor.  Again, the elevation is mostly visible, if only in limited detail.  One could guess that there is some sort of extended feature in the top where the ridge should be.

This interpolation method is called Spline.  Spline is similar to IDW in that they are both considered deterministic interpolation methods. Spline uses a mathematical formula to create a smooth surface with minimal curvature of the model.  The surface still passes through each point, but the curves between points are rounded off.  Of the methods used, this has produced the smoothest, if not the most true to life rendering our the real world surface. It shows the valley in good detail, but the ridge is still a series of spiked points.

Figure 12.  Side view of Spline model.  Much smoother than Natural Neighbor.  Peaks on ridge still noticeable.  Since all the methods show the ridge line in a similarly peaked way, this would be a good indication that our sampling is too small to gather that level of detail.

Figure 13. 3D view of Spline interpolation.  This angle gives a fairly accurate representation of the real world surface.  All the features are visible, but there is an impression of a depression taking place above the ridge line where there should only be an even plain.

Figure 14.  2D model using
the Spline interpolation method.  We have a good idea where most of the features are.  However, the data shows the depression and the central valley to be nearly the same depth, this is not shown well in this method.

The last method used was a Triangular Irregular Network, or TIN. TIN's use a network edges of the points to create triangles.  The result is a series of contiguous, non-overlapping triangles.  This gives us what we see in figure 15.

Figure 15.  TIN method from the top.
Looks a little strange, but the
detail is there, just not smooth.

As a part of this exercise we were to look at our terrain model and see if there were areas that needed to be resurveyed.  Our group made the decision that the top part of our model could use more detail to get the ridges to stand out more.  So back out into the cold we went. The decision was made to double the points along the Y axis on about a third of the area.

Figure 16. New excel data with
more points added to Y axis.

It took a little more massaging of the data in excel, but we were able to add decimal numbers so that we could add a coordinate at .5 as seen in figure 16.

Of the five methods of interpolation that we worked with, I think Spline was the most accurate in showing detail of our terrain model.

This was the method I used the second time with the new data.  Figure 17 shows the new spline 3D model and next to it is the original model with the old data.

Figure 17. Old survey data, less detail on ridge in top third.  In this model we see that the ridge has not taken the shape of a sideways Y, but is closer to and arch shape.  On the edges of the ridge it almost looks like there is a valley, but that is not now is appears in the real world.

Figure 18. Spline model with new survey data.  You can see some more detail in the top third of the map when compared to the old survey data.  Here it looks more like the sideways Y that is in the actual surface, but it is still not as much like a ridge as it should appear.

Conclusion

In the future it may be better to collect more points from the beginning.  This would give us better detail in the resulting images than what we created in our survey.  Any interpolation method is only as good as the data that is backing it up.  The ideal resolution is relative to the study area, which was very small in our case and was only meant as in introduction to spatial concepts.  It should be noted that it is easier to whittle down the amount of data if you have too much, than it is to make guesses with poor data.

Another way to improve the accuracy of the model would be to make the features larger so they show better to begin with.  Our ridge was rather narrow for the resolution we were collecting, this resulted in spikes and peaks, rather than a smooth ridge surface running across our plain.  Our valley was really more of a trench as the sides were very steep and, while this can be seen well in the Natural neighbor(figure 9) and IDW(figure 3) methods it didn't show well in Kriging(figure 6), and it is not very smooth overall.

I found that spline gave the best visual representation of the data we collected, although there are still gaps and differences between what is shown and what was there in the real world model.  It maintains accuracy by still passing through all the points, but it minimizes curves to allow for a smooth model which lends well to the human eye.




Sources of information:

ESRI - Interpolating Surfaces in ArcGIS Spatial Analyst
    http://webapps.fundp.ac.be/geotp/SIG/interpolating.pdf

Methods of Generating Surfaces In Environmental GIS Applications
    http://proceedings.esri.com/library/userconf/proc95/to100/p089.html

ESRI - ArcGIS Help Online
    http://resources.arcgis.com/en/home/